1. Field of the Invention
The present invention generally relates to processes, computer programs and systems, methods of making them and methods of using them for improving the determination of one or more digestive effects upon an ingestable substance. The underlying data used in this determination may originate from either an in vitro or in vivo analysis. The processes may be either partially or fully manual or automated, and combinations thereof.
2. Related Art
U.S. Pat. No. 6,651,012 relates to techniques used in connection with determinating a health indicator (HI) of a component, such as that of an aircraft component. Techniques are described for estimating data values as an alternative to performing data acquisitions, as may be used when there is no pre-existing data.
U.S. Pat. No. 6,645,834 relates to a product and method of treating failure of passive immunity transfer and for stimulating growth and milk production in cows by administration of proteins purified from bovine colostrum is disclosed. Also administration in spray dried form as a diet supplement to growing calves or adult cows improves growth and milk production due to the presence of previously unappreciated nonspecific proteins.
U.S. Pat. No. 6,575,905 relates to a real-time glucose estimator using a linearized Kalman filter to determine a best estimate of glucose level in real time. The real-time glucose estimator can be implemented using a software algorithm.
U.S. Pat. No. 6,539,311 relates to an apparatus and method for measuring chemical, biological, nuclear agents in an environment includes several detectors capable of measuring concentrations of the agents in the environment and a processor capable of operating an algorithm which, based on two sequential measures of concentration of the agent, estimates decay or elevation rate of the concentrations of the agent and inputs this estimated change rate to a Kalman filter which predicts the next measurement.
U.S. Pat. No. 6,440,447 relates to the present invention concerns a method of enhancing milk production by a ruminant that includes providing a feed that contains sorbitol and at least one additional feed component, and orally feeding the feed to the ruminant.
U.S. Pat. No. 6,413,223 relates to a device for noninvasive, continuous monitoring of arterial blood pressure for advanced cardiovascular diagnoses. Simulation results indicate that the approach can generate an accurate estimation of the arterial blood pressure in real-time even from noisy sensor signals.
U.S. Pat. No. 6,384,384 relates to boil dry conditions are detected in utensils heated on a cooking appliance having at least one energy source disposed under a cooking surface such as a glass-ceramic plate and a controller for controlling the level of power supplied to the energy source. In one preferred embodiment, the portion of the controller that generates the derivative estimates is implemented as two Kalman filters.
U.S. Pat. No. 6,357,429 relates to the apparatus for estimating the richness of a mixture admitted into each of the combustion chambers of an engine having injectors comprising a sensor supplying an output signal that varies in substantially linear manner with richness and that is placed at the junction point between the exhausts from the chambers, and also comprises calculation means. The behavior model includes a submodel specific to each combustion chamber and having, for the chamber of order i, a Kalman filter having a coefficient matrix Cij and a specific gain matrix Kij, where i corresponds to the number of the chamber and j corresponds to the number of the weighting coefficient.
U.S. Pat. No. 5,955,122 relates to methods of altering blood constituents in grazing animals. Improvement in body condition and body weight is concomitant with reduced milk production.
U.S. Pat. No. 5,767,080 relates to a method for enhancing milk production in dairy cows is disclosed herein. The method comprises feeding dairy cows a feed ration comprising silage made from corn plants that are homozygous for at least one bm gene and, coextensively in time, administering biologically active somatotropin to the cows.
U.S. Pat. No. 5,687,733 relates to cardiac output is separately estimated in a local estimator and a trend estimator to provide the cardiac output values. The local estimator preferably provides initial values to start a trend estimator.
U.S. Pat. No. 5,534,271 relates to a process for improving the utilization of feedstuffs by a ruminant, the process comprising the steps of mixing a lactic acid producing bacteria culture and a lactate utilizing bacteria culture, admixing these cultures with a dry formulation or an animal feedlot diet into a composition, and administering this composition orally to ruminants. The composition of the process is in a dry powder form for storage at ambient temperatures for long durations.
U.S. Pat. No. 5,313,212 relates to a radar system including a Kalman filter that processes radar return signals to produces position, velocity, acceleration, gain and residual error output signals, and a post-processor that processes these signals in accordance with a track filter bias estimation procedure.
U.S. Pat. No. 5,115,391 relates to making use of the conceptual and computational similarities between the Karmarkar method and the Kalman filter in a controller system that is capable of handling the observer function, the minimum time controller function and the minimum energy controller function. Different controls applied to the Kalman filter structure element and to the other elements of the system yielding control signals for control tasks.
U.S. Pat. No. 4,893,262 relates to a weight feeding system using a stochastic controller wherein the weight of material is sensed, and an estimate of the mass flow state of the material being discharged is created by use of a Kalman filter process. Feedback control tuning is also employed to monitor the set-point error in order to achieve quick response while maintaining smooth steady-state set point control.
S. Noftsger and N. R. St-Pierre, (2003), J. Dairy Sci. 86:958-969. Metabolizable protein (MP) supply and acid balance were manipulated through selection of highly digestible rumen-undegradable protein (RUP) sources and methionine (Met) supplementation. The supplementation of Met did not improve the efficiency of utilization during the digestibility study. Other results indicated that post-ruminal digestibility of RUP and amino acid balance can be more important than total RUP supplementation.
M. E. McCormick, D. D. French, T. F. Brown, G. J. Cuomo, A. M. Chapa, J. M. Fernandez, J. F. Beatty, and D. C. Blouin, (1999), J. Dairy Sci., 82:2697-2708. A study to determine the effects of excess dietary crude protein (CP) and rumen undegradable protein (RUP) on reproduction and lactation performance of Holstein cows. Feeding grain diets that contained excess dietary protein impaired the reproductive performance of dairy cows grazing ryegrass.
Marshall D. Stern, Alex Bach, and Sergio Calsamiglia, (1997), J. Anim. Sci., 75:2256-2276. Because in vivo measurement of nutrient digestion in the rumen and small intestine requires ruminally and intestinally cannulated animals that are expensive, labor-intensive, and subject to error associated with markers and inherent animal variation, alternative techniques have been developed. Researchers have proposed various in situ or in vitro procedures for estimating ruminal and small intestinal nutrient digestion. This review summarizes these alternative techniques.
Alex Bach. Marshall D. Stern. Neal R. Merchen, and James K. Drackley, (1998), J. Anim. Sci., 76:2885-2893. A linear model, two mathematical nonlinear models, and a curve-peeling procedure were used to estimate rate and extent of ruminal CP degradation of meat and bone mean (MBM) and soybean mean (SBM) from data obtained using the in situ Dacron polyester bag technique.
Sergio Calsamiglia and Marshall D. Stern, (1995), J. Anim. Sci., 73:1459-1465. A three-step in vitro procedure was developed to estimate intestinal digestion of proteins in ruminants. Because of variation, differences in intestinal digestion of proteins among and within various sources should be considered when determining protein value for ruminants.
C. A. Zimmerman, A. H. Rakes, T. E. Daniel and B. A. Hopkins, (1992), J. Dairy Sci., 75:1954-1964. Soybean meal enhanced with rumen undegradable protein shows improved yields of milk and its components in primiparous cows fed low fiber diets, even when high protein diets were fed.
All documents cited herein are incorporated by reference for all purposes.
Background of the Technology
Analytical Chemistry in Studying Digestion
The study of digestion, while integral to all aspects of agriculture, has traditionally been difficult to address within the context of analytical chemistry. The digestive process is very complex in any organism, but particularly so in multi-cellular organisms wherein large variations in digestive effects occur at different stages in the process.
Collecting in vivo data is usually a very expensive undertaking for evaluating the degradability of an ingestable substance, particularly when the stage of the digestive process under analysis occurs entirely within the body of a subject. On the other hand, an in vitro model of a digestion can be very complex as it is necessary to incorporate a myriad of factors affecting any stage of the digestive process under analysis. Also, the data produced by either an in vitro or in vivo analysis will often be unreliable as the results can vary extensively in the degree of precision and accuracy that is achieved in the analysis due to the large number of factors that can affect the digestion of a substance after it has been ingested.
This difficulty in gathering accurate and precise data is compounded in any digestion process analysis using sequentially applied in vitro models for each stage of digestion. This is done to determine the overall digestive effects upon an ingested substance and will involve an in vitro model of each individual digestion stage. As data will ordinarily be gathered at each stage, this compounds the problem in assessing accuracy and precision from the data produced by the overall in vitro model.
Ruminant Digestion
The digestion of a ruminant (e.g., a cow) has been a subject of interest throughout history, but until recent times was guided almost exclusively by empirical observations. Only in recent years have there been any serious efforts to analyze the mechanics of the ruminant digestive process using analytical chemistry. This is due to the complexity and wide variations occurring in this particular type of digestive system.
The ruminant digestive process is focal to many aspects of modern agriculture. A major economic concern in dairy farming is the conversion of feedstuffs to milk. Likewise, the conversion of feed to meat guides decision-making in planning the ruminant diet in raising livestock for producing meat products. Also, the goal in producing both dairy and meat products is the efficient conversion of dietary feed, and the economic use of nutrients supplied by feedstuffs. Thus a more informed assessment of the effects a feed mixture will have upon a ruminant will impact decision-making for all the agricultural processes to which it is connected. Also ancillary to these goals is the environmental impact of the farming and feeding plans.
The increasing use of supplementary feeds has led to greater interest in cow nutrition and how best to meet these requirements. But, feeding strategies are often enigmatic to implement as the ruminant digestive process is unpredictable and difficult to calibrate for any given mix of feed. No simple answer or single recipe for feeding cows will suit all desired outcomes. Cow nutrition can be quite complex, the basic goal being to ascertain what the ruminants require and how best to meet these needs in a cost-effective and practical way. All sources of feed will eventually come under consideration: pasture, silage, hay, fodder crops, grains, pellets and by-products, as well as trace elements and mineral premixes. Forage, either preserved (hay, silage) or fed as pasture generally makes up the majority of the dairy cow diet, so the challenge is to evaluate and manage the feed process to be able to balance this diet using an array of feeding materials.
Three steps are involved in ruminants obtaining nutrients from their diet. First is ingestion, which is the physical act of taking food into the body. This is followed by digestion, in which the food is mechanically and chemically broken down to simpler chemical compounds. Finally, absorption occurs allowing some nutrients to pass from the digestive system into the blood stream.
The digestive system of the ruminant is well adapted to a diet of plant material. As ruminants, cows have one true stomach (the abomasum) and three other compartments (the rumen, the reticulum and the omasum), each having a specific role in the breakdown of the feed consumed. A representative ruminant digestive system is shown in FIG. 1. Once food has been ingested, it is briefly chewed and mixed with saliva, swallowed and passed down the esophagus into the rumen.
Ruminant Digestive Physiology
The rumen is the largest compartment of the adult ruminant stomach. It is adapted for the digestion of fiber and is sometimes described as a “fermentation vat.” Its internal surface is covered with tiny projections called papillae; these increase the surface area of the rumen and allow better absorption of some digested nutrients, notably volatile fatty acids. The reticulum is separated from the rumen by a ridge of tissue. Its lining has a raised honeycomb-like pattern, also covered with small papillae. In an adult cow, the rumen and reticulum together have a capacity of about 50 to 120 liters of food and fluid.
The temperature inside the rumen remains stable at around 39° C. (38-42° C.) which is suitable for the growth of a range of micro-organisms. These microbes break down a feed mixture through a fermentation process. Under normal conditions, the pH of the contents of the rumen and reticulum is maintained in the range of 6-7, although it may be lower in grain-fed cows. The stable pH range is maintained by continual removal, via the rumen wall, of acidic end products of microbial fermentation, and by the addition of bicarbonate from the saliva. Saliva has several roles, including that it makes chewing and swallowing easier, but primarily, it has a chemical function deriving from it containing sodium (Na) and potassium (K) salts acting as buffering agents against acidity. A cow can produce 150 liters or more of saliva daily and the volume secreted depends upon the time to be spent eating and ruminating.
Before food reaches the rumen its breakdown has already begun by the mechanical action of chewing. Chemical breakdown is initiated by enzymes produced by the microbes in the rumen. The walls of the rumen and reticulum move continuously, churning and mixing the ingested feed with the rumen fluid (or ‘digestive chemicals’) and microbes. The contractions of the rumen and reticulum improve the flow of finer food particles into the next chamber, the omasum.
Rumination, or chewing the cud, is the process whereby newly eaten feed is returned to the mouth for further chewing. This extra chewing breaks the feed down into smaller pieces, thereby increasing its surface area. The smaller surface area in turn makes the feed more accessible to the chemicals which break it down. As a result, the rate of microbial digestion in the rumen is increased. The amount of time spent ruminating depends on the fiber content of the feed. The more fiber in the feed, the longer the ruminating time, therefore the less feed that can be eaten overall, and the less overall conversion to dairy or meat products. When any food is eaten by the cow, the predominant nutrients are initially in the form of carbohydrates, proteins and fats (or lipids). These are digested to products which can be used directly by the cow or by the microbes in the rumen.
Carbohydrate Digestion
Plant tissue dry matter is about 75% carbohydrate by weight. Microbial fermentation breaks the carbohydrates down into simple sugars. The microbes use these sugars as an energy source for their own growth and for making end products which are used by the cow. The end products of microbial fermentation of carbohydrates include: volatile fatty acids (mainly acetate, propionate and butyrate) and gases (carbon dioxide and methane). All carbohydrates can be fermented by rumen microbes, but the soluble and storage forms (starches) are fermented more quickly than the structural forms. Sugars and starches are broken down easily and quickly. By comparison, cell-wall material is digested slowly. As plants mature their cell walls become lignified. The lignin reduces the availability and utilization of structural carbohydrates. In other words, as plants mature their digestibility declines because the components of their cell walls become less accessible and harder to digest.
Soluble carbohydrates are digested 100 times faster by the microbes in the rumen than are storage carbohydrates, and storage carbohydrates are digested about five times faster than the structural carbohydrates. The bacteria which digest structural carbohydrates, such as cellulose and hemicellulose, produce a large proportion of acetic acid, which is important in the production of milkfat. These bacteria are sensitive to fats and acidity in the rumen. If a feed mixture contains too much fat or if the rumen becomes too acidic through feeding rapidly digestible carbohydrates, these bacteria can be completely eliminated or their growth rate inhibited. Reduction or elimination of these bacteria not only reduces the digestibility of the feed, it may also reduce the intake of feed. Once structural carbohydrates have passed through the rumen, there is little likelihood that they will be broken down further.
The bacteria that digest storage carbohydrates, or the starchy feeds such as cereal grains or potatoes are quite different from the cellulose-digesting bacteria. They are less sensitive to acidity and produce mainly propionic acid. Starches are rapidly fermented, and the lactic and propionic acid they produce causes acidity to increase in the rumen. The acidity caused by excess starch-digesting bacteria can suppress the bacteria which digest cellulose and thus reducing milkfat production. The bacteria that ferment feeds high in soluble sugars such as molasses, beets, turnips and good quality grass are similar to those that ferment starch. Sugary feeds generally cause fewer problems with increased acidity in the rumen than starchy feeds.
The most important end products of carbohydrate breakdown in the rumen are volatile fatty acids (VFAs). These acids are important because they are the major source of energy for the ruminant. The proportions in which they are produced determine fat and protein content of milk. The three major volatile fatty acids produced are acetate, propionate and butyrate. The ratio of the various VFAs produced depends on the type of feed being digested. Volatile fatty acids are absorbed through the walls of the rumen then transported in the bloodstream to the liver. In the liver they are converted to other sources of energy. From the liver, the energy produced is used to perform various functions such as milk production, maintenance of body systems, pregnancy and growth.
Lipid Digestion
Lipids (i.e., fats) are also a source of energy for the ruminant. Fats are either partially degraded and biohydrogenated in the rumen or assume a bypass or protected form. Fats are present in most of the more common dairy feeds in relatively small amounts. Protected fats, those which escape microbial digestion in the rumen, can be used to overcome the digestive upsets caused by high levels of rumen-degradable fat. The protected fats are readily digested and absorbed across the wall of the small intestine.
Protein Digestion
Protein, when digested, is broken down into peptides which are short chains of amino acids. Further digestion of peptides yields individual amino acids and eventually ammonia. The protein used by the ruminant may be from the feed mixture (dietary protein) or from the microbes washed from the rumen (microbial protein). The amount of each type depends on the extent to which dietary protein is degraded in the rumen and on the growth and outflow of microbes from the rumen.
Microbes in the rumen break down the rumen degradable protein (RDP) to amino acids then to ammonia. Ammonia is a major source of nitrogen for microbial growth. The microbes also convert non-protein nitrogen into ammonia. Microbes are continually ‘flushed’ from the reticulo-rumen, through the omasum to the next chamber, the abomasum, where they die and are digested by the cow. The amino acids produced when microbial protein is digested are then absorbed through the small intestine. The amount of microbial protein flowing to the intestines depends on the availability of energy and ammonia in the cows diet. If energy is limited, microbes become less efficient at using ammonia. Instead of being converted to microbial protein, the ammonia is absorbed across the rumen wall and into the bloodstream. In the liver, ammonia is then converted to urea. Most of this urea is excreted in the urine and some is recycled back into the rumen as non-protein nitrogen in saliva. When energy is in excess relative to protein, the rate of microbial protein synthesis declines. Total protein supply to the cow is reduced and milk yield and milk protein yield decreases. Excess energy is converted to body conditioning rather than to milk production.
Generally, pasture-based diets are relatively high in protein. The dietary protein that is directly available to the cow is rumen undegradable protein (RUP). A valuable proportion of this protein is then digested in the abomasum and small intestine. RUP provides a greater diversity of amino acids than does protein found in microbes.
Rumen degradable protein (RDP) is any protein in the diet that is broken down (digested) and of potential use by the microbes in the rumen. If enough energy (particularly carbohydrate) is available in the rumen, most of the digested RDP will be used to produce microbial protein. Undegradable dietary protein (RUP) is any protein in the diet that is not digested in the rumen. A variable proportion of RUP is dependent on the source and is digested in the lower gut.
The proportion of the protein in the diet which bypasses rumen digestion, and becomes RDP varies depending on how well the protein is protected from the microbes. This is shown diagrammatically in FIG. 2. A feed mixture can be treated with heat or chemicals to protect the protein. However, it is possible to over-protect protein and it then moves through the entire gut and out the other end without being digested. The RDP of feed also depends on how much is eaten in total, and how quickly the feed flows through the rumen. Greater intake and faster flow-through mean more protein becomes RDP because it simply escapes through the rumen before microbial breakdown occurs.
Factors Affecting Digestion
Some nutrients are absorbed across the rumen wall. Absorption involves the movement of individual feed components through the wall of the digestive tract into the blood stream by which they are transported to the liver. There is a constant flow of digestive material through the digestive tract. The passing of material through the rumen affects the extent of digestion. Generally, the rate of passage depends on density, particle size, ease of digestion and level of feeding. Some foods pass through the ruminant digestive system fairly quickly, but very indigestible food may be excreted over a long period.
The micro-organisms or microbes in the rumen include bacteria, protozoa and fungi. Bacteria and protozoa are the most significant microbes. Billions of bacteria and protozoa are found in the rumen where they digest dry matter in the feed mixture. Different species of bacteria and protozoa perform different functions. The numbers and proportions of each type of microbe depend on the individual animal's diet. Maintaining a proper mixture of different microbes is essential for keeping the rumen functioning efficiently. Dietary changes can cause a rapid change in the microbial population, which will also change the fermentation pattern and interfere with fiber digestion. Adjusting the level of grain fed must be done gradually so that the populations of rumen microbes can adjust accordingly. The speed of digestion of feeds depends on the quality and composition of the feed. It is also affected by the number and type of microbes, the pH in the rumen, the nutrients limiting the growth of the microbes, and the removal of microbes from the rumen. Energy and protein are the major nutrients which limit microbial growth and therefore rumen fermentation. The microbial population needs energy and protein for growth and multiplication. If either of these nutrients is in short supply, microbial growth is retarded, and so is the rate of digestion (the ruminal digestibility) of feed.
The omasum lies between the reticulum and abomasum. The material entering the omasum is made up of 90-95 percent cent water. The primary function of the omasum is to remove some of this water and to further grind and break down feed.
The abomasum connects the omasum to the small intestine. Acid digestion, rather than microbial fermentation, takes place in the abomasum, much the same as in the human stomach. The lining of the abomasum is folded into ridges which produce gastric juices containing hydrochloric acid and enzymes called pepsins. The pH of these gastric juices varies from 1 to 1.3 making the abomasum very acid, with a pH of about 2. The acidity in the abomasum kills the rumen microbes. The pepsins carry out the initial digestion of microbial and dietary protein in the abomasum.
From the abomasum the digested food moves to the small intestine. There, enzymes continue the digestion of feeds and microbes. Most nutrient absorption occurs in the small intestine. The large intestine, mainly the caecum and colon, is the site of secondary fermentation, particularly of fiber. Absorption of water, minerals and ammonia also occurs here. The components of feed not digested in the large intestine are passed through the rectum and anus and then expelled as waste.
Ruminant Diet Formulation
Formulating a diet is an important part of any feeding strategy. It is a means of meeting production and financial goals by feeding to the specific requirements of the ruminant in the most economical way. To formulate a diet, the skilled artisan needs to know the quantity of nutrients the cow or herd needs to meet production and animal health goals, and the nutrient content of the feeds. A balanced diet is one in which the animal nutrient requirements equals the nutrients available in the diet both from fermentation or direct digestion by the animal. Another consideration in balancing diet is whether the animal is physically able to eat the amount of feed intended to be provided. The final consideration is economics in that the economic response from feeding specific nutrients must exceed their cost.
Dietary requirements are calculated based upon production goals. Factors to consider are meat and milk production and composition, animal activity, weight, stage of pregnancy and changes in body condition. Diet formulation is largely a set of mathematical procedures combined with observation of the ruminant. The ruminant's ability to produce milk or enhanced body condition for meat depends largely on the feed eaten in terms of the intake of protein, energy and fiber. The feed must first be digested and the products of digestion absorbed into the blood from the digestive tract. How the animal uses or partitions the products of digestion are for maintenance, activity, pregnancy, milk production or body condition.
There are a range of products from the digestion of feeds consumed by the ruminant animal. These include ammonia, carbon dioxide, methane, volatile fatty acids, fats, undigested fiber, rumen microbes and undegradable protein. Some products of digestion are wasted, including carbon dioxide, methane, undigested fiber, and some are used by the animal. Fats from the diet or biosynthesized primarily from acetate by the liver, glucose from gluconeogenesis in the liver using predominantly propionate as the main precursor, and amino acids from post-ruminally digested microbial protein and RUP, circulate in the cow's blood stream ready for their role in metabolic processes. This is illustrated schematically in FIG. 3.
Milk is produced by udder tissue. About 500 liters of blood pass through the udder to produce one liter of milk. Blood delivers water, glucose, fats and amino acids to the udder. Cells in the udder tissue use these substances to form and secrete milk. Water in the milk comes from water in the blood. Lactose, milk sugar, is produced from the glucose, itself made from propionate in the liver. Milkfat comes from absorbed dietary fats, from de-novo synthesis using acetate as substrate and released body fat in the blood.
Milk protein, which is mostly casein, is built from the amino acids digested and absorbed from microbes and rumen undegradable protein in the blood using ATP (adenosine triphosphate) as an energy source to build the milk protein. The level of fat and protein in milk varies, depending on the breed of cow, stage of lactation, and the diet. It follows, then, that the dollar value of milk varies too.
The udder makes milk protein from the amino acids and energy sources carried in the blood. Amino acids are the building blocks, and ATP provides the energy. ATP is derived from the catabolism of organic molecules by the alveolar cells. Sometimes amino acids are in catabolized to generate ATP as a source of energy. This is not an efficient use of feed because it wastes the protein-producing potential of the amino acids. Conversely, if ATP supply is plentiful but amino acids are in short supply or their relative supply is imbalanced, the building of milk protein will be limited. Any surplus of glucose may produce some lactose, but most will be stored; that is, the cow will put on body weight rather than produce milk. This also is not an efficient use of feed.
Milk protein and lactose production, and therefore milk volume, are related because milk protein and lactose serve as osmotic regulators in milk. The quantity of amino acids and the amount of glucose in the blood, ready for protein and lactose production, tend to be related to each other due to diet. A diet higher in energy often produces more rumen microbes, which are digested to amino acids; and a high-energy diet also produces more propionate, which converts to glucose. On the other hand, a diet higher in fiber often produces less microbes and more acetate, which converts to fats. Amino acids can be broken down to glucose if there is a shortage of glucose, but the reverse cannot occur.
Analytical Methods for Studying Digestion
The total amount of protein available for absorption is dependent upon the flow of microbial and dietary protein to the duodenum and also the intestinal digestibility of each type of protein source. It is possible to obtain estimates of the intestinal digestibility of any ingestable substance, including protein, using either in vivo or in vitro methodology. The in vivo methods, especially those for testing the digestive effect of regions below the first areas of the stomach are time-consuming, labor-intensive and require the use of surgically prepared animals. In vitro methods address some of these limitations by simulating various physiological conditions in the digestion of ruminants and other types of animals. One in vitro method, the Minnesota Three-Step Method was developed by Calsamiglia and Stern in 1995 (Calsamiglia et al., J. Anim. Science, v. 73: 1459-1465) and simulates two segments of the ruminant digestive process, Pepsin Digestion and Intestinal Digestion, using in vitro techniques, while a third area, the rumen itself, is tested using an in situ technique. This combination of techniques when calibrated properly is effective at roughly determining from the overall dietary protein in a given feed mixture the amount and percentage of rumen protein (RUP) in the dietary feed mixture and then the portion of the determined RUP that is then digested in the intestine (dRUP).
Precision and Accuracy
The individual test results of the directly measured RUP and dRUP of any feed mixture using these in vivo, in situ, and in vitro techniques tend to vary as the precision of the assay is poor. This calls into question the accuracy of any single result, and the potential that all results may be inaccurate depending upon how the methodology is calibrated. In all experimental measurements, there is a degree of uncertainty. This is usually dependent upon, among other things, the limitations of the measuring instrument or the skill of the person making the measurement. The instruments' built-in or inherent errors are called systematic errors. If a scale is not calibrated correctly, it will yield a reading that is consistently too high or too low. When errors are introduced by the skill or ability to read the scientific instruments, this will lead to results that may be either to high or too low. These are called random errors.
Although all experimental measurements are subject to error, the total number of repeated or related measurements can be evaluated in terms of their precision and accuracy. Precision indicates the reproducibility of a measurement. That is, the closeness in agreement among the values when the same quantity is measured several times. If the series of measurements is reproducible, then good precision is obtained as careful inspection of each measurement deviates only by a small amount from the average of the series. On the other hand, if there is a wide deviation among the series of measurements the precision is poor. A measurement is said to be accurate if it is close to the known “accepted” or “most probable” value. For example, the boiling point of pure water at sea level is 100° C. However a series measurements clustered very near 95° C. would be precise, since these figures show a high reproducibility yet inaccurate. However, the values are considerably off from the accepted value of 100° C. So, the measurements are not accurate.
On the other hand, a series of measurements averaging 100° C., but varying between 80° C. and 120° C. would be accurate yet imprecise. In this set of measurements, suspected inaccuracy may arise from a systemic error such as a mis-calibrated thermometer.
Statistical Sampling
A sample is a subset of a population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available. Inferential statistics generally require that sampling be random although some types of sampling, such as those used in voter polling, seek to make the sample as representative of the population as possible by choosing the sample to resemble the population on the most important characteristics.
A biased sample is one in which the method used to create the sample results in samples that are systematically different from the population. It is important to realize that it is the method used to create the sample not the actual make up of the sample itself that defines the bias. A random sample that is very different from the population is not biased: it is by definition not systematically different from the population. It is randomly different.
Standard Deviation and Variance
The formula for the standard deviation is very simple: it is the square root of the variance. It is the most commonly used measure of the spread in data. The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable. Many formulas in inferential statistics use the standard deviation.
The variance is a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean. The formula (in summation notation) for the variance in a population is:
      σ    2    =            ∑                          ⁢                        (                      X            -            μ                    )                2              N  where μ is the population mean and N is the number of scores or measurements. When the variance is computed in a sample from a population, the statistic:
      S    2    =            ∑                          ⁢                        (                      X            -            M                    )                2              N  (where M is the mean of the sample) can be used.
However S2 is a biased estimate of σ2. A statistic is biased if it consistently over or underestimates the parameter it is estimating. In other words, it is biased if its expected value is not equal to the parameter. A stop watch that is a little bit fast gives biased estimates of elapsed time. Bias in this sense is different from the notion of a biased sample. A statistic is positively biased if it tends to overestimate the parameter; a statistic is negatively biased if it tends to underestimate the parameter. An unbiased statistic is not necessarily an accurate statistic. If a statistic is sometimes much too high and sometimes much too low, it can still be unbiased. But it would be very imprecise.
By far the most common formula for computing variance in a sample is:
      s    2    =            ∑                          ⁢                        (                      X            -            M                    )                2                    N      -      1      which gives an unbiased estimate of σ2. Since samples are usually used to estimate parameters, s2 is the most commonly used measure of variance.Regression Analysis
Regression is used to quantify the relationship between two or more continuous variables and to make predictions regarding the value of the dependent variables based on the levels of the independent variables. These predictions are made possible by knowing something about the values predicted. In other words, based on existing data values, predictions are made about other, similar values. Linear regression is used to make predictions about a single value. Simple linear regression involves discovering the equation for a line that most nearly fits the given data. That linear equation is then used to predict values for the data.
A regression equation is a mathematical equation that can be used to predict the values of one dependent variable from known values of one or more independent variables. Correlation describes the strength, or degree, of a linear relationship. That is, correlation allows the user to specify to what extent the two variables behave alike or vary together. Correlation analysis is used to assess the simultaneous variability of a collection of variables. The relationships among variables in a correlation analysis are generally not directional.
In order to make predictions, the user must examine the distribution of the data given. From this data, the user can then make a prediction about the problem being assessed. A predictor variable can be defined as a variable which is used to estimate some characteristic or response. A regression analysis which involves only one predictor is called simple linear regression analysis. Even though a single predictor may oversimplify the estimation in real systems, the results that are obtained can be easily extended to real systems.
The general regression equation can be written as y=a+b x. In order to predict a variable, the user needs to find the mean, variance, deviation and standard deviation of the values of x and y. The constants a and b in the regression equation are called the regression coefficients. The value of the constants a and b in the regression equation can be found out from the following two equations:a=Y−bX b=(Σxy−(Σx)(Σy)/n)/(Σx2−(Σx)2/n).When the values of a and b are found, the regression equation can be written using these values. The regression line is the equation of the line of best fit for the data available. In other words, the error, which is the sum of the square of the vertical distance of each of the points from the regression line, is the smallest using this line.
Multiple regression is used to make predictions from multiple continuous variables. Use of multiple regression involves the discovering of the relationship between the values and then finding an equation that satisfies that relationship which considers if the variables are dependent or not. The equation has the form:k=ax+by+cz. This is called the regression equation of k on x, y and z. And the type of regression model is called a multiple regression model.
If there is a linear relationship between a dependent variable z and two independent variables x and y. Then there exists an equation connecting the variables which has the formz=a+bx+cy. This is called a regression equation of z on x and y. If x is the dependent variable, a similar equation would be called a regression equation of x on y and z.Bayesian Statistics
Bayesian approaches use prior probabilities in conjunction with observations to estimate posterior probabilities, resulting in higher accuracy than is possible with classical statistical techniques. Thus, the variability and uncertainty in data and decisions, inherent in a complex food chain, can be dealt with.
From the early part of this century until the 1970s there was basically only one theory of statistical inference, the frequentist approach. The modern Bayesian approach began as a serious alternative in the 1960s and 1970s. In the 1990s, new computational procedures have even made Bayesian methods the only viable approach for some important kinds of problems involving navigation and space travel.
The main distinguishing feature of the Bayesian approach is that it makes use of more information than the frequentist approach. Whereas the latter is based on analysis of what we could call ‘hard data’, that is data which are generally well-structured and derived from a well-defined observation process, Bayesian statistics also accommodates ‘prior information’ which is usually less well specified and may even be subjective. This makes Bayesian methods potentially more powerful, but also implies a need for extra care in their use.
Kalman Filtering
In 1960s, R. E. Kalman developed an approach using Bayesian methods to describe a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application in the area of autonomous or assisted navigation.
The Kalman filter is a set of mathematical equations that provides an efficient computational recursive solution of the least-squares method. The filter is very powerful in several aspects: it supports estimations of past, present, and future states, and it can do so even when the precise nature of the modeled system is unknown. The Kalman filter has been used to solve problems in areas of engineering such as control systems to aircraft tracking via radar. It is a technique for accurately estimating the state of a dynamic system using a recursive algorithm. A general representation of how the Kalman filter is applied is shown in FIG. 4.
The main advantage of the Kalman filter algorithm over other adaptive algorithms is that it has a much faster rate of convergence to the optimal solution. It is also highly applicable to processing via a microprocessor thus it offers advantages to real-time applications such as those mentioned above. However, it has not been used in the unrelated field of agriculture or as a means of controlling or estimating agricultural production.